Options
Pairs of positive solutions of a quasilinear elliptic Neumann problem driven by the mean curvature operator
Omari, Pierpaolo
2025
Abstract
We establish the existence of multiple positive weak solutions of the quasilinear elliptic Neumann problem driven by the mean curvature operator ( −div ∇u/ p 1 + |∇u|2 _ = λw(x) |u|p−2u in Ω, −∇u ν/ p 1 + |∇u|2 = 0 on ∂Ω. Here, Ω is a bounded regular domain in RN, with N ≥ 2, p ∈ (1, 1∗), w is a sign-changing weight function, and λ > 0 is a parameter. Our findings provide the existence, for sufficiently small λ, of two positive solutions, the smaller in C1(Ω), the larger in BV (Ω), which respectively bifurcate from (λ, u) = (0, 0) and from (λ, u) = (0,+∞). This way we extend to a genuine PDE setting some results obtained in [22, 23] for the corresponding one-dimensional problem.
Source
Pierpaolo Omari, "Pairs of positive solutions of a quasilinear elliptic Neumann problem driven by the mean curvature operator" in: "Rendiconti dell’Istituto di Matematica dell’Università di Trieste: an International Journal of Mathematics vol.57 (2025)", EUT Edizioni Università di Trieste, Trieste, 2025, pp.
Languages
en
Rights
Attribution-NonCommercial-NoDerivatives 4.0 International
File(s)